Parabolicity and rigidity of spacelike hypersurfaces immersed in a Lorentzian Killing warped product

Eudes L. de Lima; Henrique F. de Lima; Eraldo A. Jr. Lima; Adriano A. Medeiros

Commentationes Mathematicae Universitatis Carolinae (2017)

  • Volume: 58, Issue: 2, page 183-196
  • ISSN: 0010-2628

Abstract

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In this paper, we extend a technique due to Romero et al. establishing sufficient conditions to guarantee the parabolicity of complete spacelike hypersurfaces immersed into a Lorentzian Killing warped product whose Riemannian base has parabolic universal Riemannian covering. As applications, we obtain rigidity results concerning these hypersurfaces. A particular study of entire Killing graphs is also made.

How to cite

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de Lima, Eudes L., et al. "Parabolicity and rigidity of spacelike hypersurfaces immersed in a Lorentzian Killing warped product." Commentationes Mathematicae Universitatis Carolinae 58.2 (2017): 183-196. <http://eudml.org/doc/288217>.

@article{deLima2017,
abstract = {In this paper, we extend a technique due to Romero et al. establishing sufficient conditions to guarantee the parabolicity of complete spacelike hypersurfaces immersed into a Lorentzian Killing warped product whose Riemannian base has parabolic universal Riemannian covering. As applications, we obtain rigidity results concerning these hypersurfaces. A particular study of entire Killing graphs is also made.},
author = {de Lima, Eudes L., de Lima, Henrique F., Lima, Eraldo A. Jr., Medeiros, Adriano A.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {Lorentzian Killing warped product; complete spacelike hypersurfaces; parabolic spacelike hypersurfaces; entire Killing graphs},
language = {eng},
number = {2},
pages = {183-196},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Parabolicity and rigidity of spacelike hypersurfaces immersed in a Lorentzian Killing warped product},
url = {http://eudml.org/doc/288217},
volume = {58},
year = {2017},
}

TY - JOUR
AU - de Lima, Eudes L.
AU - de Lima, Henrique F.
AU - Lima, Eraldo A. Jr.
AU - Medeiros, Adriano A.
TI - Parabolicity and rigidity of spacelike hypersurfaces immersed in a Lorentzian Killing warped product
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2017
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 58
IS - 2
SP - 183
EP - 196
AB - In this paper, we extend a technique due to Romero et al. establishing sufficient conditions to guarantee the parabolicity of complete spacelike hypersurfaces immersed into a Lorentzian Killing warped product whose Riemannian base has parabolic universal Riemannian covering. As applications, we obtain rigidity results concerning these hypersurfaces. A particular study of entire Killing graphs is also made.
LA - eng
KW - Lorentzian Killing warped product; complete spacelike hypersurfaces; parabolic spacelike hypersurfaces; entire Killing graphs
UR - http://eudml.org/doc/288217
ER -

References

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